Number Systems
Coordinate Geometry - Graphing
Operations
Properties
Exponents (Integer and Rational)
Factoring
Rational Expressions
Radicals
1. How are numbers classified?
2. How is set builder notation and interval notation used?
3. Find the distance from, and the midpoint between given two points.
4. How is the order of operations used?
5. How are factoring patterns recognized and applied?
6. How are expressions simplified?
7. How are exponents (including rational and negative) used properly?
8. How are radicals simplified?
1. Perform simple operations with whole numbers. fractions, and decimals with and without the use of variables
2. Recognize and apply factoring patterns.
3. Use interval and set builder notation properly.
4. Use exponents (including rational and negative)properly.
5. Simplify expressions (polynomial and raitonal).
6. Simplify radicals.
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald
(same text used all year)
1. Which points lie on the graph of a given figure?
2. Find the center, radius, or equation given information about a circle.
3. How are equations and solved (including absolute value equations)?
4. How are inequalities solved (including absolute value inequalities)?
5. How are rational equations and inequalities solved?
6. How are systems solved
1. Recognize which points are part of a graph 2. Be able to find the center, radius, or equation given information about a circle.
3. Solve equations that are linear, quadratic, and polynomial (including absolute value and rational).
4. Solve inequalities that are linear or quadratic(including absolute value).
5. Solve systems by substitution, liear combination, graphing.
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald
Chapter 2
Quiz 2.1-2.3
Test 2.1-2.4A
Quiz2.4-2.6
Quiz 2.7
Quiz 2.8
Test Chapter 2
November - December
1. Functions
2. Domain and Range
3. Linear Functions
4. Parent Functions
1. What is a function?
2. How/when is function notation used?
3. How is a value evaluated and what does it mean?
4. How is the domain of a function determined from a graph or equation?
5. Find the proper form of all types of linear equations (standard, point-slope, slope-intercept) given certain information.
6. Change from standard, point-slope, slope-intercept form to any other form.
7. What are the 9 Parent functions? How are they graphed? Give the domain, range, interval of increase/decrease.
1. Determine if a relation is a function from graph or from its equation.
2. Write proper function notaion.
3. Evaluate the function and be able to tell what this means in the contest of the probelm.
4. Find an equation of a line given 2 points, a point and the slope, point and a parallel or perpendicular line.
5. Be able to change from standard, point-slope, slope-intercept form to any other form.
6. Know all 9 Parent functions, their graphs, domain, range, interval of increase/decrease.
7. Know which graphs are even/odd?
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald
More on Chapter 3 - Functions
Combination and Compostion of Functions
Inverses
One-to-one Functions
Piecewise Functions
Quadratic Functions,
Variation
1. How are functions combined? What restrictions are necessary?
2. What results in the compostion of functions? What is the domain of the composition? Use values to evaluate the function.
3. How do we find the inverse of a function? What is the domain and range of the inverse?
4. What does it mean for functions to be one-to-one?
5. How are piecewise functions graphed?
6. What makes a function quadratic?
7. What are the differnt forms of a quadratic function and when/why is each one used?
8. What is an example of a direct variation? inverse variation?
1. Given a function, students should be able to combine functions (using addition, subtraction, multiplication, division), determine the domain of the combination, and evaluate the function when given a value for the variable.
2. Find the composition of functions and give the domain.
3. Find the inverse of a function, graphically and algebraically; give the domain and range of the inverse.
4. Determine if a function is one-to-one from its graph or its equation.
5. Graph piecewise functions.
6. Find standard form, vertex form, and intercept form for a quadratic function and graph.
7. Find a variation equation (direct or inverse) and use it apply to a given set of conditions.
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald
Polynomials:
Combining Polynomials
Synthetic Division
Polynomial Long Division
Graphing Polynomials
Writing Equations of a polynomial function from a graph
Rational Functions:
Find the domain of the rational function
Find all asymptotes, intercepts, holes
Write the limit notation that describes the end behavior of the graph and the behavior near a vertical asymptote
Writing Equations of a rational function from a graph
1. What is a polynomial? What is not?
2. What process is used when adding, subtracting, multiplying polynomials?
3. When is long division or synthetic division used?
4. What are the essential questions before graphing a polynomial? How does the leading coefficient, degree, types of factors change the shape of the graph?
5. Given the polynomial, whether in standard from or factored form, how is it graphed?
6. What is a rational function?
7. What are the essential questions before graphing the rational function? How does the leading coefficient, degree, types of factors change the shape of the graph?
8. Given the rational function, in standard form or factored form, how is it graphed?
9. How are the asymptotes and intercepts found?
10. What is the limit notation is used for the end behavior /and behavior near a vertical asymptote?
1. Identify the degree, leading coefficient, constant of a polynomial. Recognize when terms do not constitute a polynomial.
2. Be able to apply addtion, subtraction, multiplication techniques to find a polynomial.
3. Perform long and synthetic division to find the quotient and the remainder.
4. Graph a polynomial when it is given in factored form or standard form.
5. Recognize a rational function.
6. Determine the domain, intercepts, asymptotes of a rational function.
7. Write the end behavior of the rational function and behavior near any vertical asymptote using limit notation.
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald
Teacher Generated workshee
Quiz(zes) (1-2) on Polynomials;
Test on Polynomials
Quizzes (2-3) on Rational Functions;
Test on Rational Functions
March - April
Exponential Functions:
The One-to-one property
Exponential Identities
Graphs of the exponential functions
Translations of the graphs of exponential functions
Compound Interest problems
Continuously Compounded Interest
Logarithms:
Inverse properties of logarithms and exponents
Natural logarithms
Common logarithms
Simple computations with and without a calculator
Using logarithms to solve equations and solve problems
1. What is an exponential function? How is it graphed?
2. What is the one-to-one property?
3. What are the properties / identities for exponential functions?
4. How is interest compounded or population growth determined?
What determines if the interest is compounded continuously?
5. What is a logarithmic function? How is it graphed?
6. What is the relationship between an exponential and a logarithmic function?
7. What are the properties / identities for logarithmic functions?
8. How are logarithms used when solving problems?
1. Sketch the graph of an exponential function with intercepts and asymptote.
2. Solve equations using the one-to-one property.
3. Compute the amount of money in an account when compounded over time.
4. Find the population when growth or decay has occurred.
5. Sketch the graph of a logarithmic function with intercepts and asymptote.
6. Solve equations using common or natural logarithms.
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald Teacher Generated worksheets
Test on Exponential Functions
Quizzes (2-3) on Logarithmic Functions;
Test on Logarithmic Functions
April - May
Trigonometric Ratios
Rigth Triangle Definitions of Trigonometric Functions
Identities:Ratio, Pythagorean, Cofunction
Angle of Elevation and angle of depression
Development of the Unit Circle.
Using the Unit Circle for exact values of sine, cosine, and tangent.
1. What are the six trigonometric ratios for a given angle?
2. How do I find the angle given the sine, cosine, or tangent?
3. Given a specific trig ratio, how do I find the others?
4. How do you solve a right triangle?
5. How are trig ratios used to solve real life problems?
6. How are the Law of Sines or Law of Cosines used when the triangle is not a right triangle?
7. How does this all translate to the Unit Circle?
8. What are the exact values for the sine,cosine, and tangent on the Unit Circle?
1. Find the trigonometric function values for an acute angle in a right triangle.
2. Find the trigonometric function value for an acute angle given information about other trigonometric values.
3. Find an exact value for a trigonometric function of a special acute angle.
4. Solve a right triangle.
5. Use the Law of Sines and the Law of Cosines and determine when to use which formula.
6. Translate exact values to the Unit Circle.
7. Learn exact values for sine, cosine, and tangent for the Unit Circle.
Text: College Algebra and Trigonometry, A Contemporary Approach (2nd ed.) Dwyer & Greenwald
Teacher Generated worksheets
Quiz on Right Triangles;
Quiz on Law of Sines and Law of Cosines;
Quiz on Special Values;
Test on Triangle Trigonometry;
Quiz(zes) on Unit Circle Values
Table of Contents
August-
September
Coordinate Geometry - Graphing
Operations
Properties
Exponents (Integer and Rational)
Factoring
Rational Expressions
Radicals
2. How is set builder notation and interval notation used?
3. Find the distance from, and the midpoint between given two points.
4. How is the order of operations used?
5. How are factoring patterns recognized and applied?
6. How are expressions simplified?
7. How are exponents (including rational and negative) used properly?
8. How are radicals simplified?
2. Recognize and apply factoring patterns.
3. Use interval and set builder notation properly.
4. Use exponents (including rational and negative)properly.
5. Simplify expressions (polynomial and raitonal).
6. Simplify radicals.
(same text used all year)
Quiz #2: 1.5-1.6
Quiz #3: 1.5-1.7A
Quiz #4: 1.7-1.8
Test - Chapter 1
September - November
2. Find the center, radius, or equation given information about a circle.
3. How are equations and solved (including absolute value equations)?
4. How are inequalities solved (including absolute value inequalities)?
5. How are rational equations and inequalities solved?
6. How are systems solved
3. Solve equations that are linear, quadratic, and polynomial (including absolute value and rational).
4. Solve inequalities that are linear or quadratic(including absolute value).
5. Solve systems by substitution, liear combination, graphing.
Chapter 2
Test 2.1-2.4A
Quiz2.4-2.6
Quiz 2.7
Quiz 2.8
Test Chapter 2
November - December
2. Domain and Range
3. Linear Functions
4. Parent Functions
2. How/when is function notation used?
3. How is a value evaluated and what does it mean?
4. How is the domain of a function determined from a graph or equation?
5. Find the proper form of all types of linear equations (standard, point-slope, slope-intercept) given certain information.
6. Change from standard, point-slope, slope-intercept form to any other form.
7. What are the 9 Parent functions? How are they graphed? Give the domain, range, interval of increase/decrease.
2. Write proper function notaion.
3. Evaluate the function and be able to tell what this means in the contest of the probelm.
4. Find an equation of a line given 2 points, a point and the slope, point and a parallel or perpendicular line.
5. Be able to change from standard, point-slope, slope-intercept form to any other form.
6. Know all 9 Parent functions, their graphs, domain, range, interval of increase/decrease.
7. Know which graphs are even/odd?
Teacher Generated worksheets
Quiz Parent Functions
Parent Functions Project
January
Combination and Compostion of Functions
Inverses
One-to-one Functions
Piecewise Functions
Quadratic Functions,
Variation
2. What results in the compostion of functions? What is the domain of the composition? Use values to evaluate the function.
3. How do we find the inverse of a function? What is the domain and range of the inverse?
4. What does it mean for functions to be one-to-one?
5. How are piecewise functions graphed?
6. What makes a function quadratic?
7. What are the differnt forms of a quadratic function and when/why is each one used?
8. What is an example of a direct variation? inverse variation?
2. Find the composition of functions and give the domain.
3. Find the inverse of a function, graphically and algebraically; give the domain and range of the inverse.
4. Determine if a function is one-to-one from its graph or its equation.
5. Graph piecewise functions.
6. Find standard form, vertex form, and intercept form for a quadratic function and graph.
7. Find a variation equation (direct or inverse) and use it apply to a given set of conditions.
Teacher Generated Worksheets
Quiz - Inverses, One-to-one Functions, Piecewise Functions, Quadratic Functions
Test - Combining Functions, Composition, Inverses, One-to-one Functions, Piecewise Functions, Quadratic Functions, Variation
February - March
Combining Polynomials
Synthetic Division
Polynomial Long Division
Graphing Polynomials
Writing Equations of a polynomial function from a graph
Rational Functions:
Find the domain of the rational function
Find all asymptotes, intercepts, holes
Write the limit notation that describes the end behavior of the graph and the behavior near a vertical asymptote
Writing Equations of a rational function from a graph
2. What process is used when adding, subtracting, multiplying polynomials?
3. When is long division or synthetic division used?
4. What are the essential questions before graphing a polynomial? How does the leading coefficient, degree, types of factors change the shape of the graph?
5. Given the polynomial, whether in standard from or factored form, how is it graphed?
6. What is a rational function?
7. What are the essential questions before graphing the rational function? How does the leading coefficient, degree, types of factors change the shape of the graph?
8. Given the rational function, in standard form or factored form, how is it graphed?
9. How are the asymptotes and intercepts found?
10. What is the limit notation is used for the end behavior /and behavior near a vertical asymptote?
2. Be able to apply addtion, subtraction, multiplication techniques to find a polynomial.
3. Perform long and synthetic division to find the quotient and the remainder.
4. Graph a polynomial when it is given in factored form or standard form.
5. Recognize a rational function.
6. Determine the domain, intercepts, asymptotes of a rational function.
7. Write the end behavior of the rational function and behavior near any vertical asymptote using limit notation.
Teacher Generated workshee
Test on Polynomials
Quizzes (2-3) on Rational Functions;
Test on Rational Functions
The One-to-one property
Exponential Identities
Graphs of the exponential functions
Translations of the graphs of exponential functions
Compound Interest problems
Continuously Compounded Interest
Logarithms:
Inverse properties of logarithms and exponents
Natural logarithms
Common logarithms
Simple computations with and without a calculator
Using logarithms to solve equations and solve problems
2. What is the one-to-one property?
3. What are the properties / identities for exponential functions?
4. How is interest compounded or population growth determined?
What determines if the interest is compounded continuously?
5. What is a logarithmic function? How is it graphed?
6. What is the relationship between an exponential and a logarithmic function?
7. What are the properties / identities for logarithmic functions?
8. How are logarithms used when solving problems?
2. Solve equations using the one-to-one property.
3. Compute the amount of money in an account when compounded over time.
4. Find the population when growth or decay has occurred.
5. Sketch the graph of a logarithmic function with intercepts and asymptote.
6. Solve equations using common or natural logarithms.
Quizzes (2-3) on Logarithmic Functions;
Test on Logarithmic Functions
April - May
Rigth Triangle Definitions of Trigonometric Functions
Identities:Ratio, Pythagorean, Cofunction
Angle of Elevation and angle of depression
Development of the Unit Circle.
Using the Unit Circle for exact values of sine, cosine, and tangent.
2. How do I find the angle given the sine, cosine, or tangent?
3. Given a specific trig ratio, how do I find the others?
4. How do you solve a right triangle?
5. How are trig ratios used to solve real life problems?
6. How are the Law of Sines or Law of Cosines used when the triangle is not a right triangle?
7. How does this all translate to the Unit Circle?
8. What are the exact values for the sine,cosine, and tangent on the Unit Circle?
2. Find the trigonometric function value for an acute angle given information about other trigonometric values.
3. Find an exact value for a trigonometric function of a special acute angle.
4. Solve a right triangle.
5. Use the Law of Sines and the Law of Cosines and determine when to use which formula.
6. Translate exact values to the Unit Circle.
7. Learn exact values for sine, cosine, and tangent for the Unit Circle.
Teacher Generated worksheets
Quiz on Law of Sines and Law of Cosines;
Quiz on Special Values;
Test on Triangle Trigonometry;
Quiz(zes) on Unit Circle Values